Function automorphism_group 

pub fn automorphism_group(
    graph: &Graph,
    colors: Option<&[u32]>,
) -> IgraphResult<Vec<Vec<u32>>>

Compute a generating set of the automorphism group Aut(G).

Returns a small list of permutations that generate the whole group: every automorphism of graph is a product of these generators (and their inverses). Each generator g is a vertex permutation given as a Vec<u32> where g[v] is the image of vertex v; it preserves adjacency and, when supplied, vertex colours. This mirrors igraph’s igraph_automorphism_group, which likewise returns generators rather than the full (potentially factorial) group.

The generating set is not unique — different correct implementations (and igraph’s bliss backend) may return different generators. What is invariant is the group they generate: its order equals count_automorphisms. The trivial group (only the identity) is represented by an empty list.

colors is an optional per-vertex colour slice (length must equal the vertex count); only colour-preserving permutations are included. Pass None for an uncoloured graph.

Generators come from the shared individualization-refinement engine (see canonical_permutation): every leaf of the I-R search tree whose certificate equals the canonical one yields one automorphism, and a greedy subset that generates all of them is returned.

Scope

Simple graphs (directed or undirected), self-loops allowed, optional vertex colours. Multi-edges are rejected.

Errors

Returns an error if colors has the wrong length or the graph has multiple edges between the same pair of vertices.

Examples

use rust_igraph::{Graph, automorphism_group};

// The path P_3 (0-1-2) has one non-trivial automorphism: the end swap
// (0 2). So a single generator suffices.
let mut p3 = Graph::new(3, false).unwrap();
p3.add_edge(0, 1).unwrap();
p3.add_edge(1, 2).unwrap();
let gens = automorphism_group(&p3, None).unwrap();
assert_eq!(gens, vec![vec![2, 1, 0]]);